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1 year ago

Find the inverse of each function. Is the inverse a function? f(x)=x⁷

Mathematics

1 answer:

Luda [366]1 year ago

3 0

The inverse of the function x^7 is x^-7 and it is also a function.

An inverse function or an anti function is defined as a function, which can reverse into another function.

A standard method to find inverse of a function is to set y=f(x)

let y= f(x)=x^7

thus

$\sqrt[7]{y}$ =x

thus $f^{-1}$ (y)= $\sqrt[7]{y}$

thus $f^{-1} (x)=\sqrt[7]{x}$

(To verify this if a function is inverse or not we are required to check for the identity)

f( $f^{-1}$ (x))= $f^{-1}$ (f(x))=x

Therefore, The inverse of the function x^7 is x^-7 and it is also a function.

For further reference:

brainly.com/question/2541698?referrer=searchResults

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Answer:

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Step-by-step explanation:

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3 years ago

If h = 3.7 then what is 0.8 + h?

Gnoma [55]

H=3.7
Then 0.8+h=0.8+3.7
=4.5

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4 years ago

ASAP AWARDING MAJOR POINTS Determine the symbols(+,-,*. And division) to be placed in each ⭕️ the first one must be simplified t

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Hope this helps. :)

7 0

3 years ago

Read 2 more answers

A small company is creating a new product to sell to buyers. They have estimated that it will cost them $6 to produce each item

miv72 [106K]

Answer:

$347,600

Step-by-step explanation:

There is fixed startup cost of 242,000 no matter how many units they product.

Also, each unit costs 6 to produce, so to produce 17,600 items, it's going to cost:

17,600 * 6 = 105,600

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8 0

3 years ago

A square park measures 170 feet along each side. Two paved paths run from each corner to the opposite corner and extend 3 feet i

Cerrena [4.2K]

Answer:

The total area, in square feet, taken by the paths is 2,004

Step-by-step explanation:

see the attached figure with lines to better understand the problem

I can divide the figure into four right triangles, one small square and four rectangles

step 1

Find the area of the right triangle of each corner of the path

The area of the triangle is

$A=(1/2)(b)(h)$

substitute the given values

$A=(1/2)(3)(3)=4.5\ ft^2$

step 2

Find the hypotenuse of the right triangle

Applying Pythagoras Theorem

Let

d -----> hypotenuse of the right triangle

$d^{2}=3^{2}+3^{2}$

$d^{2}=18$

$d=\sqrt{18}\ ft$

simplify

$d=3\sqrt{2}\ ft$

The hypotenuse of the right triangle is equal to the width of the path

step 2

Find the area of the small square of the path

The area is

$A=b^{2}$

we have

$b=3\sqrt{2}\ ft$ ----> the width of the path

substitute

$A=(3\sqrt{2})^{2}$

$A=18\ ft^2$

step 3

Find the length of the diagonal of the square park

Applying Pythagoras Theorem

Let

D -----> diagonal of the square park

$D^{2}=170^{2}+170^{2}$

$D^{2}=57,800$

$D=\sqrt{57,800}\ ft$

simplify

$D=170\sqrt{2}\ ft$

step 4

Find the height of each right triangle on each corner

The height will be equal to the width of the path divided by two, because is a 45-90-45 right triangle

$h=1.5\sqrt{2}\ ft$

step 5

Find the area of each rectangle of the path

The area of rectangle is $A=LW$

we have

$W=3\sqrt{2}\ ft$ ----> width of the path

Find the length of each rectangle of the path

$L=(D-2h-d)/2$

where

D is the diagonal of the park

h is the height of the right triangle in the corner

d is the width of the path (length side of the small square of the path)

substitute the values

$L=(170\sqrt{2}-2(1.5\sqrt{2})-3\sqrt{2})/2$

$L=(170\sqrt{2}-3\sqrt{2}-3\sqrt{2})/2$

$L=(164\sqrt{2})/2$

$L=82\sqrt{2}\ ft$

Find the area of each rectangle of the path

$A=LW$

we have

$W=3\sqrt{2}\ ft$

$L=82\sqrt{2}\ ft$

substitute

$A=(82\sqrt{2})(3\sqrt{2})$

$A=492\ ft^2$

step 6

Find the area of the paths

Remember

The total area of the paths is equal to the area of four right triangles, one small square and four rectangles

substitute

$A=4(4.5)+18+4(492)=2,004\ ft^2$

therefore

The total area, in square feet, taken by the paths is 2,004

3 0

3 years ago